Impedance distance relay

ABSTRACT

An apparatus for determining the peak value of the sinusoidal component of an electrical quantity which may include a nonsinusoidal component by means of comparing the first and second differential magnitudes of the electrical quantity at any time interval of the period of the sinusoidal component whereby the value of any low rate of change component is attenuated, as for example the D.C. offset which is normally present during fault conditions. The apparatus also includes means to determine the phase angles between two sinusoidal components and when such two sinusoidal components represent current and voltage to determine the magnitude of the impedance of the network energized by said sinusoidal quantities.

{22 Filed: [211 Appl. No.: 256,668

' Unitedi StateS-Patent "1191f Rockefeller, Jr. I I I I [54] IMPEDANCE DISTANCE RELAY [75] Inventor: George D; Rockefeller, Jr., Morris Plains, NJ

l [73] Assignee: Westinghouse Electric Corporation,

Pittsburgh, Pa.

7 May 25,1972

lav

VOLTAGE 4 1972 Traversi....; ..'....317 27 R 1451 May'l, 197s Primary ExaminerJames D. Trammell AttorneyA. T. Stratton et al.

57 ABSTRACT mine the magnitude of the impedance of the network energized by said sinusoidal quantities.

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1. Apparatus of the character comprising, first input terminals adapted to be energized by a first pulsating electrical quantity which has a first sine wave component having a angular frequency omega , mathematical circuitry effective to derive a first derived quantity which is proportional to the first derivative of a varying magnitude electrical quantity supplied thereto, said circuitry further being effective to derive a second derived quantity which is proportional to the second derivative of said varying quantity, connection means connecting said circuitry to said input terminals for supplying said pulsating quantity thereto, said first derived quantity being a cosine function, said second derived quantity being a sine function so that said derived quantities and said maximum magnitude of said sine wave may be represented by the sides of a right triangle in which the two shorter sides are proportional in length to the magnitudes of said derived quantities and in which the length of the longest side is proportional to the maximum magnitude of said sine wave component, and trignometric triangle solving means energized by said derived quantities for solving said triangle to determine the length of said longest side of said triangle and thereby said maximum magnitude.
 2. The combination of claim 1 in which at least one of said means includes multiplying means which multiplies its said derived quantity by a constant other than unity.
 3. The combination of claim 2 in which said constant is a funcTion of omega .
 4. The combination of claim 1 in which said first means includes multiplying means which multiplies its said derived quantity by a quantity having the ratio (1/ omega ) to provide a third derived quantity and said second means includes multiplying means which multiplies its said derived quantity by a quantity having the ratio (1/ omega ) to provide a fourth derived quantity.
 5. The combination of claim 4 in which said circuitry includes means squaring said third and fourth derived quantities, and means summing said squared quantities to provide an output quantity proportional to the square of said maximum magnitude of said sine wave component.
 6. The combination of claim 1 in which said connecting means connects and disconnects said circuitry to said input terminals for brief intervals at first and second and third instants, said approximation of said first derivative being determined by the difference in magnitude of the pulsating quantity between said first and third instants, said approximation of said second derivative being determined by the difference in the rate of change of the magnitude of said pulsating quantity between said first and second instants and between said second and third instants divided by one half of the time interval between said first and said third instants.
 7. The combination of claim 6 in which the first time interval between said first and said second instants is equal to the second time interval between said second and said third instants.
 8. The combination of claim 7 in which said first and said second time intervals are equal to (1/2 omega ).
 9. The combination of claim 8 in which the time of said brief intervals is in the order of magnitude of 10 nano-seconds.
 10. The combination of claim 8 in which theta is an angle having an arc tangent determined by the ratio of one of said derived quantities to the other of said derived quantities, said circuitry including first ratioing means energized by said derived quantities and having an output quantity proportional to said ratio to determine said angle theta , and means determining a magnitude proportional to the cosine of said angle theta .
 11. The combination of claim 10 in which said one derived quantity is the smaller of said derived quantities and said other derived quantity is the larger of said derived quantities.
 12. The combination of claim 10 in which said circuitry provides said derived quantities as algebraic quantities of a plus and minus character, a first selected derived quantity of said derived quantities being plus when theta is in the 180* sector between minus 90* and plus 90* and being negative when theta is in the 180* sector between plus 90* and plus 270*, a second selected quantity of said derived quantities which is not said first selected quantity being plus when theta is in the 180* sector between 0* and 180* and being negative when theta is in the 180* sector between 180* and 360* .
 13. The combination of claim 6 in which theta is an angle having an arc tangent determined by the ratio AA/BB and theta '' is an angle having an arc tangent determined by the ratio BB/AA, where AA is proportional to said first derived quantity and BB is proportional to said second derived quantity, theta and theta '' being the complementary angles of a right triangle, the two shorter sides of which are equal in magnitude to the magnitudes AA and BB and the longer side of which is proportional to the maximum magnitude of said sine wave component, said circuitry being operable to determine the angles theta and theta '' by dividing the smaller of AA and BB as a numerator by the larger of AA and BB as the denominator whereby the arc tangent of the determined angle remains between zero and unity.
 14. The combination of Claim 13, in which said circuitry provides said derived quantities as algebraic quantities of a plus and minus character, a first selected derived quantity of said derived quantities being of plus sign when theta is in the 180* sector between minus 90* and plus 90* and being of negative sign when theta is in the 180* sector between plus 90* and plus 270*, a second selected derived quantity of said derived quantities and which said second selected quantity is not said first selected quantity being of plus sign when theta is in the 180* sector between 0* and 180* and being of negative sign when theta is in the 180* sector between 180* and 360*, said circuitry being effective to provide said ratios as quantities which provide a signal which distinguishes the algebraic quantities AA and BB as to its numerator and denominator location and as to relative signs thereof and as to the location of said signs whereby the arc tangent of theta is determined for the angles 0*-45* and 135*-225* and 315*-260* and the arc of theta '' is determined for the angles 45*-135* and 225*-315* .
 15. The combination of claim 1 in which there is provided second input terminals adapted to be energized by a second pulsating electrical quantity which has a second sine wave component having an angular frequency omega , said connecting means connecting said circuitry to said second input terminals for supplying said second pulsating quantity thereto, said connecting means being effective to connect said circuitry to said first input terminals at first three separate instants consecutively time spaced by first and second time intervals and to connect said circuitry to said second input terminals at second three separate instants consecutively time spaced by third and fourth time intervals, said circuitry being effective to provide said first derived quantity which is proportional to the difference in magnitude of said first electrical quantity between said first and third of said first three instants divided by the sum of said first and second time intervals and to provide said second derived quantity which is proportional to the change in magnitude of said first electrical quantity between said first and said second of said first three instants divided by said first time interval plus the change in magnitude of said first electrical quantity between said second and said third of said first three instants divided by said second time interval with the sum of the addendum being divided by one half the sum of said first and second time intervals, said circuitry being effective to provide a third derived quantity which is proportional to the difference in magnitude of said second electrical quantity between said first and third of said second three instants divided by the sum of said third and fourth time intervals and to provide a fourth derived quantity which is proportional to the change in magnitude of said second electrical quantity between said first and second of said second three instants divided by said third time interval plus the change in magnitude of said second electrical quantity between said second and said third of said second three instants divided by said fourth time interval with the sum of the addendum being divided by one half the sum of said third and fourth timer intervals, said triangle solving means including means effective to divide as a numerator the smaller of said first and second derived quantities by the larger of said first and second derived quantities as a denominator to provide the arc tangent of a first angle and to divide as a numerator the smaller of said third and fourth derived quantities by the larger of said third and fourth derived quantities as a denominator to provide the arc tangent of a second angle, said circuitry being effective to provide A fifth quantity which is proportional to the cosine of said first angle and a sixth quantity which is proportional to the cosine of said second angle, said circuitry being effective to divide the product of said cosine of said second angle and the larger of said first and second derived quantities as the numerator by the product of said cosine of said first angle and the larger of said third and fourth derived quantities to provide a quantity proportional to the maximum value of said second sine component.
 16. A distance relay for an alternating potential transmission line, said relay having a first pair of input terminals energized by the potential of said line and a second pair of input terminals energized by the current of said line, calculating circuit means, means periodically connecting said calculating means to said pairs of input terminals to sample said voltage and said current at desired time periods, said calculating means being effective to provide cosine omega t quantities which closely approach the first derivative of said voltage and of said current divided by omega where omega 2 pi HZ and t time in seconds, said calculating means being effective to provide sine ( omega t) quantities which closely approach the second derivative of said voltage and of said current divided by omega 2, said calculating means also being effective to divide said sine ( omega t) voltage quantity by said cosine ( omega t) voltage quantity and thereby determine the magnitude of said tangent ( omega t) voltage quantity of a voltage right triangle and to divide said sin ( omega t) current quantity by said cosine ( omega t) current quantity and thereby determine the magnitude of said tangent ( omega t) current quantity of a current right triangle, said calculating means being further effective to solve said right triangles and thereby determine the maximum values of the sinusoidal component of said voltage and of said current in said line, said calculating means still further being effective to determine the magnitude of the angle ( omega t) of the voltage and of the current of said voltage and current samples.
 17. The combination of claim 16 in which said calculating means is effective to divide said maximum value of said voltage by said maximum value of said current to provide a quantity equal to the apparent impedance of said line, fault determining means comparing the apparent magnitude of said apparent impedance determined from sequential said samples with a predetermined magnitude to determine the presence or absence of a fault within the reach of said relay.
 18. The combination of claim 17 in which there is provided a counting means connected for actuation by said fault determining means, said fault determining means being effective to step said counting means each time said predetermined magnitude is greater than said apparent magnitude of said sample and to reset said counting means each time said predetermined magnitude is greater than said apparent magnitude of said sample, breaker trip means connected to said counting means, said counting means being effective to actuate said trip means solely at a count greater than unity.
 19. The combination of claim 18 in which said calculating means is effective to determine the magnitude of the phase angle between said voltage and current, and means determining said predetermined magnitude as a function of said phase angle.
 20. A controlling network of the character described, said network comprising, a number storage circuit having input and output connections, number supplying means connected to said storage input circuit and including a first gating means, said number supplying means being effective to supply a desired number having a first sign, a number adding circuit having first and second input circuits and an output circuit, second gating means connecting said storage output circuit to said first input circuit of said adding circuit, means for supplying add ends of both + and - signs to said second input circuit of said adding circuit and including a third gating means, fourth gating means connecting said output circuit of said adding circuit to said input connection of said storage circuit, a quantity determining circuit having an input and an output, fifth gating means connecting said output connection of said storage circuit to said input of said quantity determining circuit, and means connecting said output of said quantity determining circuit to said first gating means, said quantity determining means being effective when the number supplied to its said input is of said first sign and is of greater magnitude than said desired number to enable said first gating means to supply said desired number to said storage circuit.
 21. The combination of claim 20 in which there is provided a counter, said counter having input and output circuit means, a sign determining means, having an input and an output, means connecting said input of said sign determining means to said storage circuit for energization of said sign means as a function of the sign of the number in said storage circuit, means connecting said output of said sign means to said counter, said sign means being effective each time the number supplied to said storage circuit is of a sign different from said first sign to supply a counting signal to said counter, said sign means being effective each time the number supplied to said storage circuit is of said first sign to supply a signal to reset said counter.
 22. The combination of claim 21 in which said means which connects said sign means to said storage circuit includes a sixth gating means, and means opening said gating means in the order of said first gating means, said second gating means, said third gating means, said fourth gating means and said fifth gating means.
 23. Apparatus for determining the maximum magnitude of the sine wave component having an angular frequency omega of a complex pulsating electrical quantity, said apparatus comprising, input terminal means adapted to have said electrical quantity applied thereto, sampling means connected to said terminal means for determining the instantaneous magnitude of said quantity during a predetermined desired time interval, conversion apparatus connected to said sampling means, said conversion apparatus including means measuring a first change of magnitude of said signal during a first time period and dividing said changed magnitude by said first time period to provide a first signal approximating the rate of change of said component, said conversion apparatus also including means measuring second and third changes of magnitude of said signal during second and third succeeding time periods and dividing said second changed magnitude by said second time period to provide a second signal and said third changed magnitude by said third time period to provide a third signal and thereafter dividing the difference in magnitude of said third and second signals by the average magnitude of said second and third time periods to provide a fourth signal approximating the rate of change of said first signal, said conversion apparatus further including signal means multiplying said first signal by the magnitude (1/ omega ) and said fourth signal by the magnitude (1/ omega 2) and for thereafter adding together said multiplied and squared first and fourth signals to provide an output quantity having a fixed mathematical relationship with respect to the maximum magnitude of said sine wave component.
 24. The combination of claim 23 in which each of said time intervals approach zero magnitude whereby said first signal more nearly becomes the first derivative of said component and said fourth signal more nearly becomes the second derivative of said component.
 25. The combination of claim 24 in which said first time interval is coextensive with the time interval of said second and said third time interval.
 26. The combination Of claim 23 in which said first interval is equal to the total interval of said second time interval plus said third time interval and said first interval is coextensive with said second and said third intervals.
 27. The combination of claim 26 in which said second time interval is equal to said third time intervals.
 28. The combination of claim 27 in which said second and said third time intervals are equal to (1/2 omega ) and said first time interval is equal to (1/ omega ).
 29. Apparatus for determining the maximum magnitude of the sine wave component having an angular frequency comprising input terminal means adapted to arc said electrical quantity applied thereto, first and second electrical conversion means, means connecting said first and second means to said input terminals for obtaining first and second samples of said quantity which occur during at least first and second selected time intervals, said first conversion means being energized by said first sample and being effective to determine an approximation of the first derivative of said first sample and to convert the same to a first output signal corresponding to the product of said approximated first derivative and (1/ omega ), said second electrical conversion means being energized by said second sample and being effective to determine an approximation of the second derivative to said second sample and to convert the same to a second output signal corresponding to the product of said approximated second derivative and (-1/ omega 2), third electrical conversion means connected to said first and second conversion means for squaring each of said first and second output signals and thereafter adding said squared products to provide a third output quantity having a fixed mathematical relationship with respect to the maximum magnitude of said sine wave component.
 30. The combination of claim 29 in which said first and said second time intervals are coextensive.
 31. Apparatus for determining the maximum magnitude of the sine wave component of a complex alternating electrical quantity, having an angular velocity omega , said apparatus comprising input terminal means adapted to have said electrical quantity applied thereto, first electrical conversion means connected to said input terminals for determining an approximation of the first derivative of said quantity and converting same to a first output signal corresponding to the product of said approximated first derivative and (1/ omega ) second electrical conversion means connected to said input terminals for determining an approximation the second derivative of said quantity and converting same to a second output signal corresponding to the product of said approximated second derivative and (-1/ omega 2), third electrical conversion means connected to said first and second conversion means for squaring each of said first and second output signals and thereafter adding said squared products to provide a third output quantity, said third output quantity having a fixed mathematical relationship with respect to the maximum magnitude of said sine wave component.
 32. Apparatus for determining the impedance of an electrical circuit in which is present an alternating component of current and potential having an angular velocity omega , said apparatus comprising first input terminals adapted to be energized by the current component, second input terminals adapted to be energized by the potential component, mathematic circuitry connected to said first terminals and effective to derive a quantity which approximates the first derivative of said current component multiplied by (1/ omega ) and to derive a quantity which approximates the second derivative of said current component multiplied by (-1/ omega 2), second mathematic circuitry connected to said second terminal means effective to derive a quantity which approximates the first derivative of said potential component multiplied by (1/ omega ) and to derive a quantity which approximates the second derivative of said potential component multiplied by (-1/ omega 2), third circuitry connected to receive all of said signals and to derive a fifth quantity which approximates the magnitude of the impedance of said electric circuit as derived from said current and potential components.
 33. The combination of claim 32 in which said third circuitry comprises first and second and third portions, said first portion being effective to provide a sixth output quantity which is proportional to the ratio of said first and second quantities, said second portions being effective to provide a seventh output quantity which is proportional to the ratio of said third and fourth quantities, said third portions being actuated by said sixth and seventh quantities to provide said fifth quantity.
 34. The combination of claim 33 in which said third circuitry comprises a fourth portion including a plural number of groups of preselected signal generators, one of said output quantities being effective to select a desired one of said groups and the other of said output quantities being effective to select a desired one of said quantities of said selected group, said selected quantity of said selected group being effective to provide said fifth quantity.
 35. The combination of claim 32 in which at least one of said mathematic circuitries includes a first switching apparatus and means measuring the magnitude of the quantity supplied thereto and connected to said first input terminals through said switching apparatus, said one circuitry also including timing means actuating said switching apparatus to connect said magnitude measuring means to its said first input terminals at at least first and second instants in the wave of said current component, said first circuitry also including means determining first rate at which said supplied quantity magnitudes changes during the period between said first and second instants and multiplying said first rate by (1/ omega ) to thereby provide said quantity which approximates said first derivative, said one circuitry further including means determining a second rate at which its said first rate changes during the period between said first and second instants and multiplying its said second rate by (-1/ omega 2) to provide said quantity which approximates said derivative.
 36. The combination of claim 35 in which said timing means actuates said switching to connect and disconnect said magnitude measuring means at said first and second instants and at a third instant intermediate said first and second instants, said first rate being determined by the change in value of said quantity during a first interval which occurs between said first and said third instants and a second interval which occurs between said third and said second instants, said second rate being determined by the change in said first rate between said intervals.
 37. The combination of claim 36 in which said intervals are of duration equal to (1/2 omega ). 